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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code>.locally_linear_embedding</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-manifold-locally-linear-embedding">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.locally_linear_embedding</span></code></a></li>
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  <div class="section" id="sklearn-manifold-locally-linear-embedding">
<h1><a class="reference internal" href="../classes.html#module-sklearn.manifold" title="sklearn.manifold"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code></a>.locally_linear_embedding<a class="headerlink" href="#sklearn-manifold-locally-linear-embedding" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="sklearn.manifold.locally_linear_embedding">
<code class="sig-prename descclassname">sklearn.manifold.</code><code class="sig-name descname">locally_linear_embedding</code><span class="sig-paren">(</span><em class="sig-param">X</em>, <em class="sig-param">n_neighbors</em>, <em class="sig-param">n_components</em>, <em class="sig-param">reg=0.001</em>, <em class="sig-param">eigen_solver='auto'</em>, <em class="sig-param">tol=1e-06</em>, <em class="sig-param">max_iter=100</em>, <em class="sig-param">method='standard'</em>, <em class="sig-param">hessian_tol=0.0001</em>, <em class="sig-param">modified_tol=1e-12</em>, <em class="sig-param">random_state=None</em>, <em class="sig-param">n_jobs=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_locally_linear.py#L188"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.locally_linear_embedding" title="Permalink to this definition">¶</a></dt>
<dd><p>Perform a Locally Linear Embedding analysis on the data.</p>
<p>Read more in the <a class="reference internal" href="../manifold.html#locally-linear-embedding"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">{array-like, NearestNeighbors}</span></dt><dd><p>Sample data, shape = (n_samples, n_features), in the form of a
numpy array or a NearestNeighbors object.</p>
</dd>
<dt><strong>n_neighbors</strong><span class="classifier">integer</span></dt><dd><p>number of neighbors to consider for each point.</p>
</dd>
<dt><strong>n_components</strong><span class="classifier">integer</span></dt><dd><p>number of coordinates for the manifold.</p>
</dd>
<dt><strong>reg</strong><span class="classifier">float</span></dt><dd><p>regularization constant, multiplies the trace of the local covariance
matrix of the distances.</p>
</dd>
<dt><strong>eigen_solver</strong><span class="classifier">string, {‘auto’, ‘arpack’, ‘dense’}</span></dt><dd><p>auto : algorithm will attempt to choose the best method for input data</p>
<dl class="simple">
<dt>arpack<span class="classifier">use arnoldi iteration in shift-invert mode.</span></dt><dd><p>For this method, M may be a dense matrix, sparse matrix,
or general linear operator.
Warning: ARPACK can be unstable for some problems.  It is
best to try several random seeds in order to check results.</p>
</dd>
<dt>dense<span class="classifier">use standard dense matrix operations for the eigenvalue</span></dt><dd><p>decomposition.  For this method, M must be an array
or matrix type.  This method should be avoided for
large problems.</p>
</dd>
</dl>
</dd>
<dt><strong>tol</strong><span class="classifier">float, optional</span></dt><dd><p>Tolerance for ‘arpack’ method
Not used if eigen_solver==’dense’.</p>
</dd>
<dt><strong>max_iter</strong><span class="classifier">integer</span></dt><dd><p>maximum number of iterations for the arpack solver.</p>
</dd>
<dt><strong>method</strong><span class="classifier">{‘standard’, ‘hessian’, ‘modified’, ‘ltsa’}</span></dt><dd><dl class="simple">
<dt>standard<span class="classifier">use the standard locally linear embedding algorithm.</span></dt><dd><p>see reference <a class="reference internal" href="#rb2a5641379f7-1" id="id1">[1]</a></p>
</dd>
<dt>hessian<span class="classifier">use the Hessian eigenmap method.  This method requires</span></dt><dd><p>n_neighbors &gt; n_components * (1 + (n_components + 1) / 2.
see reference <a class="reference internal" href="#rb2a5641379f7-2" id="id2">[2]</a></p>
</dd>
<dt>modified<span class="classifier">use the modified locally linear embedding algorithm.</span></dt><dd><p>see reference <a class="reference internal" href="#rb2a5641379f7-3" id="id3">[3]</a></p>
</dd>
<dt>ltsa<span class="classifier">use local tangent space alignment algorithm</span></dt><dd><p>see reference <a class="reference internal" href="#rb2a5641379f7-4" id="id4">[4]</a></p>
</dd>
</dl>
</dd>
<dt><strong>hessian_tol</strong><span class="classifier">float, optional</span></dt><dd><p>Tolerance for Hessian eigenmapping method.
Only used if method == ‘hessian’</p>
</dd>
<dt><strong>modified_tol</strong><span class="classifier">float, optional</span></dt><dd><p>Tolerance for modified LLE method.
Only used if method == ‘modified’</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, optional (default=None)</span></dt><dd><p>If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by <code class="docutils literal notranslate"><span class="pre">np.random</span></code>. Used when <code class="docutils literal notranslate"><span class="pre">solver</span></code> == ‘arpack’.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int or None, optional (default=None)</span></dt><dd><p>The number of parallel jobs to run for neighbors search.
<code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <a class="reference external" href="https://joblib.readthedocs.io/en/latest/parallel.html#joblib.parallel_backend" title="(in joblib v0.14.1.dev0)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code></a> context.
<code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors. See <a class="reference internal" href="../../glossary.html#term-n-jobs"><span class="xref std std-term">Glossary</span></a>
for more details.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>Y</strong><span class="classifier">array-like, shape [n_samples, n_components]</span></dt><dd><p>Embedding vectors.</p>
</dd>
<dt><strong>squared_error</strong><span class="classifier">float</span></dt><dd><p>Reconstruction error for the embedding vectors. Equivalent to
<code class="docutils literal notranslate"><span class="pre">norm(Y</span> <span class="pre">-</span> <span class="pre">W</span> <span class="pre">Y,</span> <span class="pre">'fro')**2</span></code>, where W are the reconstruction weights.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="rb2a5641379f7-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>Roweis, S. &amp; Saul, L. Nonlinear dimensionality reduction
by locally linear embedding.  Science 290:2323 (2000).</p>
</dd>
<dt class="label" id="rb2a5641379f7-2"><span class="brackets"><a class="fn-backref" href="#id2">2</a></span></dt>
<dd><p>Donoho, D. &amp; Grimes, C. Hessian eigenmaps: Locally
linear embedding techniques for high-dimensional data.
Proc Natl Acad Sci U S A.  100:5591 (2003).</p>
</dd>
<dt class="label" id="rb2a5641379f7-3"><span class="brackets"><a class="fn-backref" href="#id3">3</a></span></dt>
<dd><p>Zhang, Z. &amp; Wang, J. MLLE: Modified Locally Linear
Embedding Using Multiple Weights.
<a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382</a></p>
</dd>
<dt class="label" id="rb2a5641379f7-4"><span class="brackets"><a class="fn-backref" href="#id4">4</a></span></dt>
<dd><p>Zhang, Z. &amp; Zha, H. Principal manifolds and nonlinear
dimensionality reduction via tangent space alignment.
Journal of Shanghai Univ.  8:406 (2004)</p>
</dd>
</dl>
</dd></dl>

<div class="section" id="examples-using-sklearn-manifold-locally-linear-embedding">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.locally_linear_embedding</span></code><a class="headerlink" href="#examples-using-sklearn-manifold-locally-linear-embedding" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="An illustration of Swiss Roll reduction with locally linear embedding "><div class="figure align-default" id="id9">
<img alt="../../_images/sphx_glr_plot_swissroll_thumb.png" src="../../_images/sphx_glr_plot_swissroll_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/manifold/plot_swissroll.html#sphx-glr-auto-examples-manifold-plot-swissroll-py"><span class="std std-ref">Swiss Roll reduction with LLE</span></a></span><a class="headerlink" href="#id9" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>


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